5.1-solutions

5.1-solutions - Na(gn2849 5.1 campisi(55842 This print-out...

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Na (gn2849) – 5.1 – campisi – (55842) 1 This print-out should have 5 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points Estimate the area under the graph oF f ( x ) = 4 sin x between x = 0 and x = π 3 using fve approx- imating rectangles oF equal widths and right endpoints. 1. area 2 . 355 correct 2. area 2 . 335 3. area 2 . 395 4. area 2 . 375 5. area 2 . 415 Explanation: An estimate For the area under the graph oF f on [0 , b ] with [0 , b ] partitioned in n equal subintervals [ x i - 1 , x i ] = b ( i - 1) b n , ib n B and right endpoints x i as sample points is A ± f ( x 1 ) + f ( x 2 ) + . . . + f ( x n ) ² b n . ±or the given area, f ( x ) = 4 sin x, b = π 3 , n = 5 , and x 1 = 1 15 π, x 2 = 2 15 x 3 = 1 5 x 4 = 4 15 x 5 = 1 3 π . Thus A 4 ± sin p 1 15 π P + . . . + sin p 1 3 π π 15 . AFter calculating these values we obtain the estimate area 2 . 355 For the area under the graph. keywords: area, sin Function, estimate area, numerical calculation, 002 10.0 points Estimate the area, A , under the graph oF f ( x ) = 2 x on [1 ,

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5.1-solutions - Na(gn2849 5.1 campisi(55842 This print-out...

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